M´ etodo

This section contains different SS-FBMC simulation results for both the AG FL and RL for QPSK, 16-QAM and 64-QAM modulations. We used the physical layer parameters listed in Table 7.1. Using the proposed spectrally shaped algorithm we find the guard subcarriers and allocated power values for active subcarriers in both FL and RL. Figure 7.3 shows one example solution of the power mask (linear scale, allocated power to active subcarriers) of the FL subcarriers for different QAM modulation orders.

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Based on our power constraint, the sum of all subcarrier powers is equal to 10 W. As we see QPSK has 2 fewer guard subcarriers than 16-QAM and 64-QAM. It also has lower power levels on its side subcarriers because of its greater Euclidean distance between signal points for a given Eb/N0. As we see for higher order modulations the SS

algorithm solution is more conservative, therefore in addition to more guard subcarriers, the allocated powers to the side subcarriers must be higher than in QPSK in order to increase the energy per bit to noise density ratio. In Figure 7.4 we plot the PSD (logarithmic scale) of SS-FBMC waveforms for the different modulation orders with the linear power mask shown in Figure 7.3.

Figure 7.4. FL PSDs for different QAM modulations.

The QPSK spectrum has slightly larger bandwidth and the difference between its peak power and the flat area of the PSD is smaller than in the other two QAM modulation orders. The 64 QAM PSD is interesting in that it is atypical for FBMC, with nulls and

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sidelobes. In Figures 7.5 and 7.6 similar results are plotted for the RL. Here the number of guard bands is smaller because in the RL the DME power is lower than in the FL.

Figure 7.5. RL subcarriers power mask for different QAM modulations.

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In the following Figures in this section (Figures 7.7 to 7.12) we plot simulated BER results for both FL and RL and different QAM modulation orders. In these figures the colored curves depict the BER performance of each individual subcarrier. The black solid and dashed curves are BER results for AWGN theoretical and the average BER across all subcarriers, respectively. We have plotted the BER result for each subcarrier to show the variation of the BER across subcarriers as a result of the spectral shaping technique.

As seen in these figures, the colored BER curves that are to the left of the dashed average BER line are the BER results for the subcarriers with higher allocated powers. Most of the BER results for the “central” subcarriers are crowded near the average BER dashed line, some to the left, and some to the right. In all of these results we do not see any error floors, even at high SNR values. We emphasize again that all these colored curves are shown simply to illustrate the BER variation that results from our spectral shaping technique.

Figure 7.7. FL QPSK BER results, colored curves are the BERs of each subcarrier and the dashed curved is the averaged BER of all subcarriers.

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Figure 7.8. FL 16-QAM BER results, colored curves are the BERs of each subcarrier and the dashed curved is the averaged BER of all subcarriers.

Figure 7.9. FL 64-QAM BER results, colored curves are the BERs of each subcarrier and the dashed curved is the averaged BER of all subcarriers.

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Figure 7.10. RL QPSK BER results, colored curves are the BERs of each subcarrier and the dashed curved is the averaged BER of all subcarriers.

Figure 7.11. RL 16-QAM BER results, colored curves are the BERs of each subcarrier and the dashed curved is the averaged BER of all subcarriers.

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Figure 7.12. RL 64-QAM BER results, colored curves are the BERs of each subcarrier and the dashed curved is the averaged BER of all subcarriers.

Generally it is the average BER (dashed curve) that matters most, although in some applications, some data can be made more reliable via careful allocation to subcarriers. To validate these results we changed the power allocation mask values very slightly and noticed that for different guard subcarrier locations, some of these subcarriers had an error floor which would also yield an error floor in the overall average BER.

As an example of a system performance differences between a conventional FBMC system [4] and SS-FBMC, we simulated the same FL link for 16-QAM and depict the result in Figure 7.13. Here the average BER reaches an error floor due to the poor performance of the subcarriers nearest the two sides of the spectrum. The SS-FBMC result for this case as shown in Figure 7.8 significantly improves the BER results and eliminates the error floors.

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Figure 7.13. FL 16-QAM BER results from FBMC, colored curves are the BERs of each subcarrier and the dashed curved is the averaged BER of all subcarriers.

According to these results, in comparison to conventional FBMC [4], our example L-band AG SS-FBMC system has a larger number of data subcarriers (2 more) and hence larger throughput (~3%) in RL QPSK, but it has more guard subcarriers (2) and slightly smaller throughput (~3%) compared to the original FBMC scheme for FL QPSK. We emphasize again that the primary virtue of the SS-FBMC design is that there is no BER floor at high SNR values.